S. David Promislow

Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift

Abstract We extend the work of Browne (1995) and Schmidli (2001), in which they minimize the probability of ruin of an insurer facing a claim process modeled by a Brownian motion with drift. We consider two controls to minimize the probability of ruin: (1) investing in a risky asset and (2) purchasing quota-share reinsurance. We obtain an analytic expression for the minimum probability of ruin and the corresponding optimal controls, and we demonstrate our results with numerical examples.

Postulates for the internal rate of return of an investment project

Abstract The internal rate of return of a finite sequence of cash flows is studied in terms of four natural postulates: (1) continuity of the rate with respect to the cash flows; (2) monotonicity, i.e. the rate increases in case any cash flow increases; (3) normalization, or agreement with the usual rate of return in the case of loan contracts; (4) scale invariance. Measure-theoretic models are constructed that satisfy the postulates. Classical rate of return functions are reconstructed within this framework and logical relationships among all these functions are established.

The probability of ruin in a process with dependent increments

Abstract We generalize some results of Gerber concerned with the probability of ruin in a linear model. In particular, we remove the boundedness restriction for the underlying distribution, allow for a weaker convergence condition for the coefficients in the infinite order case, and relax the stationarity requirement of the model.

Supermodular Functions on Finite Lattices

The supermodular order on multivariate distributions has many applications in financial and actuarial mathematics. In the particular case of finite, discrete distributions, we generalize the order to distributions on finite lattices. In this setting, we focus on the generating cone of supermodular functions because the extreme rays of that cone (modulo the modular functions) can be used as test functions to determine whether two random variables are ordered under the supermodular order. We completely determine the extreme supermodular functions in some special cases.

Purchasing Term Life Insurance to Reach a Bequest Goal while Consuming

We determine the optimal strategies for purchasing term life insurance and for investing in a risky financial market in order to maximize the probability of reaching a bequest goal while consuming from an investment account. We extend Bayraktar and Young (2015) by allowing the individual to purchase term life insurance to reach her bequest goal. The premium rate for life insurance,

Equity and Credibility

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Purchasing Term Life Insurance to Reach a Bequest Goal: Time-Dependent Case

, serves as a parameter to connect two seemingly unrelated problems. As the premium rate approaches

Decomposition properties of dual choice functionals

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Axioms for the valuation of payment streams: A topological vector space approach

, covering the bequest goal becomes costless, so the individual simply wants to avoid ruin that might result from her consumption. Thus, as

“A Re-examination of the Joint Mortality Function,” Heekyung Youn, Arkady Shemyakin, and Edwin Herman, January 2002

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